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Two roads have crossed each other at right angles. An observer P is at a distance of 30 m from the crossing O. A car is moving towards the crossing O at a speed of 16 m/s and at the same time emitting sound wave at a frequency 192 Hz. When the car is at a distance of 40 m from the crossing, the frequency of sound received by the observer is (velocity of sound in still air = 320 m/s)

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200 Hz

236 Hz

220 Hz

210 Hz

answer is A.

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Detailed Solution

$cosθ = \frac{OC}{CP} = \frac{40}{\sqrt{40^{2} + 30^{2}}} = \frac{4}{5}$

$∴ f = \frac{f_{0}}{(1 - \frac{v_{c} cosθ}{v})} = \frac{192}{(1 - \frac{16}{320} x \frac{4}{5})} Hz$

$\Rightarrow f = 200 Hz$

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